I had a plumbing problem needing to be addressed (people: stop mixing copper with cast iron piping!) and learned how to sweat (solder) copper piping. Why do they call it sweating instead of soldering? I have no idea, since I'm not a plumber, but I've done a decent enough job at sweating the copper that I have no leaks in my basement (anymore).
I don't know everything, as you'll see I'm a little short on details, good tips, good practices, background info, or plumbing code (did I mention I'm not a plumber). But hopefully it's good enough to get you started on your next project. Have fun!
Step 1: Start With a Freshly Cut Copper Pipe.
Depending how bad you cut the pipe (the best thing I had at the time was an angle grinder), you'll end up with a crappy looking end with burrs.